Beyond evidence synthesis: A meta-analytic framework for explaining heterogeneous dynamic parameters

Meta-analysis is traditionally used to synthesize evidence across independent studies. This presentation illustrates a nonstandard application of Stata’s multivariate meta-analysis framework to investigate parameter heterogeneity estimated from firm-level dynamic models. The empirical motivation comes from corporate finance, where heterogeneous adjustment dynamics make pooled panel specifications with numerous interactions difficult to interpret. I first estimate fully heterogeneous error-correction models for individual firms, obtaining firm-specific parameters measuring the speed of leverage adjustment, the sensitivity to free cash flow, and debt-maturity interaction, together with their estimated standard errors. Rather than treating these parameters as final estimates, I use Stata’s multivariate random-effects meta-regression to explain their cross-sectional heterogeneity through firm characteristics, contractual features, and institutional changes. I demonstrate how Stata’s meta commands can be extended beyond their conventional role of evidence synthesis to provide a flexible second-stage modeling framework for heterogeneous parameter estimates. The approach accommodates multiple correlated outcomes, accounts for estimation uncertainty through inverse-variance weighting, and avoids the overparameterization that often arises in pooled interaction models. Although illustrated using a novel dataset on corporate debt covenants extracted from SEC filings, the methodology is applicable to any context in which unit-specific parameters are estimated in a first stage and subsequently related to observed characteristics.